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Encoders,DecoderDemultiDemulti
Shr
rs,Multiplexers and iplexersiplexers
Prepared By:
Shruti Khatri
ObjecObjec
• Decoders• Encoders• Encoders• Multiplexers• DeMultiplexers
ctivesctives
Multiplexers
44
MultipMultip
A multiplexer has− N control inputsp− 2N data inputs
1 output− 1 outputA multiplexer routes (odata input to the outpudata input to the outpu
− The value of the th d t i t ththe data input tha
lexerslexers
or connects) the selected utut.control inputs determines t i l t d
5
at is selected.
5
MultipMultip
Z = A′ IData
inputs Z A .IControl
input
lexerslexers
I0 + A I1
6
I0 + A.I1
6
MultipMultip
MSB L
Z = A′.B'.I0 + A'.B.I
lexerslexers
A B F
0 0 I0
0 1 I1
1 0 I2
1 1 I1 1 I3
LSB
7
I1 + A.B'.I2 + A.B.I3
7
MultipMultip
MSB LS
Z = A′.B'.C'.I0 + A'.B'.C.IA.B'.C'.I0 + A.B'.C.I1
lexerslexersA B C FA B C F
0 0 0 I0
0 0 1 I1
0 1 0 I2
0 1 1 I3
1 0 0 I4
1 0 1 I5
1 1 0 I6
1 1 1 I7
SB
1 1 1 I7
8
I1 + A'.B.C'.I2 + A'.B.C.I3 + + A'.B.C'.I2 + A.B.C.I3
8
Demultiiplexers
99
DemultiDemultiA demultiplexer hasde u t p e e as
− N control inputs− 1 data input− 1 data input− 2N outputs
A demultiplexer routes (oA demultiplexer routes (othe selected output.
The value of the co− The value of the cothat is selected.
A demultiplexer performsA demultiplexer performsmultiplexer.
iplexersiplexers
or connects) the data input toor connects) the data input to
ntrol inputs determines the outputntrol inputs determines the output
s the opposite function of a
10
s the opposite function of a
10
DemultiDemultiO t WOut0
InI
WXY
Out1Out2
S1 S0
ZOut3
A B W
A B
A B W
0 0 I
0 1 0
1 0 0
1 1 0
iplexersiplexers
W A' B' IW = A'.B'.I
X = A.B'.I
Y = A'.B.I
Z = A.B.I
X Y ZX Y Z
0 0 0
I 0 0
11
0 I 0
0 0 I
11
Decooders
1212
DecoDeco
n-to-2n.n inputs
n to 2
Decode
• Information is represented • Decoding - the conversion
m-bit output code with n <=valid code word produces ap
• Circuits that perform decod• A decoder is a minterm geA decoder is a minterm ge
oderoder
n...
2n outputser
by binary codesn of an n-bit input code to an = m <= 2n such that each a unique output codeq pding are called decodersneratornerator
DecoDecoA decoder has
− N inputs− 2N outputs2 outputs
A decoder selects onedecoding the binary vadecoding the binary vaThe decoder generateth N i t i blthe N input variables.
− Exactly one outpcombination of th
odersoders
e of 2N outputs by alue on the N inputsalue on the N inputs.es all of the minterms of
put will be active for each
14
he inputs.What does “active” mean?
14
DecoDeco
B I0
Out0Out1O tI1A Out2Out3
msb
A B W
Active-h
A B W
0 0 1
0 1 0
1 0 0
1 1 0
odersoders
W A' B'WXY
W = A'.B'
X = A.B'YZ
Y = A'.B
Z = A.B
X Y Z
high outputs
X Y Z
0 0 0
1 0 0
15
0 1 0
0 0 1
15
DecoDeco
B I0
Out0Out1O t
msb
I1A Out2Out3
A B W
Active-l
A B W
0 0 0
0 1 1
1 0 1
1 1 1
odersoders
W (A' B')'W = (A'.B')'
X = (A.B')'WXY Y = (A'.B)'
Z = (A.B)'
YZ
X Y Z
ow outputs
X Y Z
1 1 1
0 1 1
16
1 0 1
1 1 0
16
DecoDecomsb
odersoders
1717
Decoder wDecoder w
high-levelenable
B I0
I1Aenable
Enable
I1A
En
En A B
1 0 01 0 0
1 0 1
1 1 0enabled
1 1 1
0 x xdisabled
with Enablewith Enable
WXY
Out0Out1O t Y
ZOut2Out3
W X Y Z
1 0 0 01 0 0 0
0 1 0 0
0 0 1 0
18
0 0 0 1
0 0 0 0
18
Decoder wDecoder w
B I0
I1Alow-levelenable
Enable
I1A
En
En A B
0 0 00 0 0
0 0 1
0 1 0enabled
0 1 1
1 x xdisabled
with Enablewith Enable
WXY
Out0Out1O t Y
ZOut2Out3
W X Y Z
1 0 0 01 0 0 0
0 1 0 0
0 0 1 0
19
0 0 0 1
0 0 0 0
19
Decoder-BasedCircuits (E
X Y Z C S
S = ∑m (1,2,4,7
C = ∑m (3,5,6,X Y Z C S0 0 0 0 00 0 1 0 1
3 inputs and 8 3-to-8 decoder
0 0 00 1 0 0 10 1 1 1 01 0 0 0 11 0 1 1 01 1 0 1 0
Ah d Al lh
1 1 0 1 01 1 1 1 1
Ahmad Almulhe
d Combinational Example)7)
7)
possible mintermscan be used for implementing this circuit
KFUPM 2009em, KFUPM 2009
3 to 8 D3-to-8 D
3-to-8
D0D1D2D3D
A0ADecoder D4
D5D6D7
A1A2
Ah d Al lhAhmad Almulhe
DecoderDecoder
KFUPM 2009em, KFUPM 2009
Encooders
2222
EncoEnco
.
.2n inputs
2n-to-n
Encoder
• Encoding - the opposite of d
.
.Encoder
Encoding the opposite of dm-bit input code to a n-bit outhat each valid code word pro
• Circuits that perform encodin• Circuits that perform encodin• An encoder has 2n (or fewer)
which generate the binary covaluesvalues
• Typically, an encoder converone bit that is 1 to a binary co
iti i hi h th 1position in which the 1 appea
oderoder
. n outputsr
decoding - the conversion of an
r
decoding the conversion of an tput code with n ≤ m ≤ 2n such oduces a unique output code
ng are called encodersng are called encoders) input lines and n output lines ode corresponding to the input
rts a code containing exactly ode corresponding to the ars.
8 to 3 Encode8-to-3 Encode
D7 D6
8-to-3
D0D1D2D3D
A0A
D7 D6
0 00 0
EncoderD4D5D6D7
A1A2 0 0
0 00 00 00 10 11 0
er (truth table)er (truth table)
inputs outputs
6 D5 D4 D3 D2 D1 D0 A2 A1 A06 D5 D4 D3 D2 D1 D0 A2 A1 A0
0 0 0 0 0 1 0 0 00 0 0 0 1 0 0 0 10 0 0 1 0 0 0 1 00 0 1 0 0 0 0 1 10 1 0 0 0 0 1 0 01 0 0 0 0 0 1 0 10 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 1
8 to 3 Encode8-to-3 Encode
D7 D6
8-to-3
D0D1D2D3D
A0A
10000
00
D7 D6
0 00 0
EncoderD4D5D6D7
A1A2
0000
00 0 0
0 00 00 00 10 11 0
er (truth table)er (truth table)
inputs outputs
6 D5 D4 D3 D2 D1 D0 A2 A1 A06 D5 D4 D3 D2 D1 D0 A2 A1 A0
0 0 0 0 0 1 0 0 00 0 0 0 1 0 0 0 10 0 0 1 0 0 0 1 00 0 1 0 0 0 0 1 10 1 0 0 0 0 1 0 01 0 0 0 0 0 1 0 10 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 1
8 to 3 Encode8-to-3 Encode
D7 D6
8-to-3
D0D1D2D3D
A0A
01000
10
D7 D6
0 00 0
EncoderD4D5D6D7
A1A2
0000
00 0 0
0 00 00 00 10 11 0
er (truth table)er (truth table)
inputs outputs
6 D5 D4 D3 D2 D1 D0 A2 A1 A06 D5 D4 D3 D2 D1 D0 A2 A1 A0
0 0 0 0 0 1 0 0 00 0 0 0 1 0 0 0 10 0 0 1 0 0 0 1 00 0 1 0 0 0 0 1 10 1 0 0 0 0 1 0 01 0 0 0 0 0 1 0 10 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 1
8 to 3 Encode8-to-3 Encode
D7 D6
8-to-3
D0D1D2D3D
A0A
00000
10
D7 D6
0 00 0
EncoderD4D5D6D7
A1A2
0100
01 0 0
0 00 00 00 10 11 0
er (truth table)er (truth table)
inputs outputs
6 D5 D4 D3 D2 D1 D0 A2 A1 A06 D5 D4 D3 D2 D1 D0 A2 A1 A0
0 0 0 0 0 1 0 0 00 0 0 0 1 0 0 0 10 0 0 1 0 0 0 1 00 0 1 0 0 0 0 1 10 1 0 0 0 0 1 0 01 0 0 0 0 0 1 0 10 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 1
8 to 3 Encode8-to-3 Encode
D7 D6
8-to-3
D0D1D2D3D
A0A
00000
11
D7 D6
0 00 0
EncoderD4D5D6D7
A1A2
0001
11 0 0
0 00 00 00 10 11 0
er (truth table)er (truth table)
inputs outputs
6 D5 D4 D3 D2 D1 D0 A2 A1 A06 D5 D4 D3 D2 D1 D0 A2 A1 A0
0 0 0 0 0 1 0 0 00 0 0 0 1 0 0 0 10 0 0 1 0 0 0 1 00 0 1 0 0 0 0 1 10 1 0 0 0 0 1 0 01 0 0 0 0 0 1 0 10 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 1
8 to 3 Encode8-to-3 Encode
D7 D6
8-to-3
D0D1D2D3D
A0A
D7 D6
0 00 0
EncoderD4D5D6D7
A1A2 0 0
0 00 00 00 1
Output equations:0 11 0
Note:
A0 = ?A1 = ?A2 = ?
Note:
er (equations)er (equations)
inputs outputs
6 D5 D4 D3 D2 D1 D0 A2 A1 A06 D5 D4 D3 D2 D1 D0 A2 A1 A0
0 0 0 0 0 1 0 0 00 0 0 0 1 0 0 0 10 0 0 1 0 0 0 1 00 0 1 0 0 0 0 1 10 1 0 0 0 0 1 0 01 0 0 0 0 0 1 0 10 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 1
This truth table is not complete! Why?This truth table is not complete! Why?
8 to 3 Encode8-to-3 Encode
D7 D6
8-to-3
D0D1D2D3D
A0A
D7 D6
0 00 0
EncoderD4D5D6D7
A1A2 0 0
0 00 00 00 1
Output equations:0 11 0A0 = D1 + D3 + D5 + D7
A1 = ?A2 = ?
er (equations)er (equations)
inputs outputs
6 D5 D4 D3 D2 D1 D0 A2 A1 A06 D5 D4 D3 D2 D1 D0 A2 A1 A0
0 0 0 0 0 1 0 0 00 0 0 0 1 0 0 0 10 0 0 1 0 0 0 1 00 0 1 0 0 0 0 1 10 1 0 0 0 0 1 0 01 0 0 0 0 0 1 0 10 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 1
8 to 3 Encode8-to-3 Encode
D7 D6
8-to-3
D0D1D2D3D
A0A
D7 D6
0 00 0
EncoderD4D5D6D7
A1A2 0 0
0 00 00 00 1
Output equations:0 11 0A0 = D1 + D3 + D5 + D7
A1 = D2 + D3 + D6 + D7A2 = ?
er (equations)er (equations)
inputs outputs
6 D5 D4 D3 D2 D1 D0 A2 A1 A06 D5 D4 D3 D2 D1 D0 A2 A1 A0
0 0 0 0 0 1 0 0 00 0 0 0 1 0 0 0 10 0 0 1 0 0 0 1 00 0 1 0 0 0 0 1 10 1 0 0 0 0 1 0 01 0 0 0 0 0 1 0 10 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 1
8 to 3 Encode8-to-3 Encode
D7 D6
8-to-3
D0D1D2D3D
A0A
D7 D6
0 00 0
EncoderD4D5D6D7
A1A2 0 0
0 00 00 00 1
Output equations:0 11 0A0 = D1 + D3 + D5 + D7
A1 = D2 + D3 + D6 + D7A2 = D4 + D5 + D6 + D7
er (equations)er (equations)
inputs outputs
6 D5 D4 D3 D2 D1 D0 A2 A1 A06 D5 D4 D3 D2 D1 D0 A2 A1 A0
0 0 0 0 0 1 0 0 00 0 0 0 1 0 0 0 10 0 0 1 0 0 0 1 00 0 1 0 0 0 0 1 10 1 0 0 0 0 1 0 01 0 0 0 0 0 1 0 10 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 1
8 to 3 Enco8-to-3 Enco
8-to-3
D0D1D2D3D
A0AEncoderD4
D5D6D7
A1A2
Output equations:
A0 = D1 + D3 + D5 + D7A1 = D2 + D3 + D6 + D7A2 = D4 + D5 + D6 + D7
oder (circuit)oder (circuit)
D
A0
D1D3D5D7
A1
D2D3D6D7
A2D4D5D6D7
8 to 3 Encode8-to-3 Encode
D7 D6
Two Limitations:D7 D6
0 00 0
1. Two or more inputs = 1• Example: D3 = D6 = 1• A2A1A0 = 111
0 00 0
2. All inputs = 0• Same as D0 =1
Output equations:
0 00 00 1
A0 = D1 + D3 + D5 + D7A1 = D2 + D3 + D6 + D7A2 = D4 + D5 + D6 + D7
0 11 0
er (limitations)er (limitations)
inputs outputs
6 D5 D4 D3 D2 D1 D0 A2 A1 A06 D5 D4 D3 D2 D1 D0 A2 A1 A0
0 0 0 0 0 1 0 0 00 0 0 0 1 0 0 0 10 0 0 1 0 0 0 1 00 0 1 0 0 0 0 1 10 1 0 0 0 0 1 0 01 0 0 0 0 0 1 0 10 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 00 0 0 0 0 0 1 1 1